A particle of mass 200 MeV/c² collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is
$${N \over 4}$$. The value of N is :
(Given the mass of the hydrogen atom to be 1 GeV/c²) ______ .

Two concentric circular coils, C₁ and C₂ are
placed in the XY plane. C₁ has 500 turns, and
a radius of 1 cm. C₂ has 200 turns and radius
of 20 cm. C₂ carries a time dependent current
I(t) = (5t² – 2t + 3) A where t is in s. The emf
induced in C₁ (in mV), at the instant t = 1 s is
$${4 \over x}$$. The value of x is ___ .

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $$ \to $$ B, A $$ \to $$ C and A $$ \to $$ D. The change in internal energies during these process are taken as E_AB, E_AC and E_AD and the work done as W_AB, W_AC and W_AD.
The correct relation between these parameters are :

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :